I rambled thru the Karwendel in a short 24-hour window during a business trip in '99. From Hall-in-Tirol, climbed the Grosse Bettelwurf and Speckkar (skipped traverse to Kleine - too much fresh snow and no harness), slept at Hallerangerhaus and hiked out to Scharnitz early the next morning. I would love to come back someday.
I stayed a weekend on Hallerangerhaus, that is property of my home section of the german alpine club. From there it's a 2h-hike to Bettelwurf hut. Then the traverse via Kleiner to Grosser Bettelwurf, descent on the normal route. Still there was some power left, so with Klaus I did the traverse of Speckkarspitze in addition on our route back to Hallerangerhaus in the afternoon. 12 hours on route - a great day in the mountains.